3.6: Valence Bond Theory

Introduction

Valence bond (VB) Theory has its roots in Gilbert Newton Lewis’s paper The Atom and The Molecule. Possibly unaware that Lewis’s model existed, Walter Heitler and Fritz London came up with the idea that resonance and wavefunctions contributed to chemical bonds, in which they used dihydrogen as an example. Their theory was equivalent to Lewis’s theory, with the difference of quantum mechanics being developed. Nonetheless, Heitler and London's theory proved to be successful, providing Linus Pauling and John C. Slater with an opportunity to assemble a general chemical theory containing all of these ideas. Valence bond theory was the result, which included the ideas of resonance, covalent-ionic superposition, atomic orbital overlap, and hybridization to describe chemical bonds. Valence bond theory looks at the interaction between atoms to explain chemical bonds. It is one of the two common theories that helps describe the bonding between atoms. The other theory is molecular orbital theory, which will be discussed in the next section. Take note that these are theories and should be treated as such; they are not always perfect.

Atomic Orbital Overlap

In VB theory, bonds are formed between atoms because a singly occupied atomic orbital on each atom overlaps to form a two electron bond. Dihydrogen (H₂) is a simple diatomic gas that has been used to illustrate this idea; however, let's look at Cl₂ as a simple example. Cl has seven valence electrons, and has a valence electron configuration of 3s²3p⁵. From the electron configuration, one can see that Cl has an unpaired electron in one of its p orbitals. That one unpaired electron indicates that Cl can bond once. As a general rule, in VB theory the number of unpaired electrons denotes how many bonds that atom can make. Since there is only one unpaired electron on each Cl, the 3p orbitals overlap to form a bond as shown in Figure \(\PageIndex{1}\). Lone pairs can be seen as filled atomic orbitals that don't interact or overlap. The idea of atomic orbitals overlapping works well for simple diatomic molecules, but other bonding geometries (trigonal planar, tetrahedral, etc.) can be created with pure atomic orbitals. For example, the central atom in a trigonal planar geometry has three bonds separated by \(120^{\circ}\), but bonds formed by overlap with the three p orbitals would be separated by \(90^{\circ}\).

Figure \(\PageIndex{1}\): Illustration showing the overlap of two singly occupied 3p orbitals on Cl to form a Cl-Cl bond. (CC BY-NC-SA; Catherine McCusker)

Atomic Orbital Hybridization

Atomic orbitals can be combined, or hybridized, to form a set of equivalent hybrid orbitals in the desired geometry.

Forming hybrid orbitals

1. The number of electron pairs (bonds and lone pairs) around the central atom determines the number of hybrid orbitals needed.
2. Orbitals cannot be created or destroyed. The number of atomic orbitals mixed will equal the number of resulting hybrid orbitals.
3. Always start with the s atomic orbital and add additional p and d* orbitals as needed.

Reminder

* As discussed previously, it is now known that d orbitals do not contribute significantly to bonding in main group compounds. As such, this discussion of valence bond theory and orbital hybridization will focus on the s and p orbitals.

Hybridization of s and p Orbitals

The Lewis structure of BeH₂ shows that it has two bonds and no lone pairs. We can generate two equivalent hybrid orbitals by combining the 2s orbital of beryllium and any one of the three degenerate 2p orbitals. By taking the sum and the difference of Be 2s and 2p_z atomic orbitals, for example, we produce two new orbitals with major and minor lobes oriented along the z-axes, as shown in Figure \(\PageIndex{2}\).

Figure \(\PageIndex{2}\): The position of the atomic nucleus with respect to an sp hybrid orbital. The nucleus is actually located slightly inside the minor lobe, not at the node separating the major and minor lobes.

Because the difference A − B can also be written as A + (−B), in Figure \(\PageIndex{3}\) and subsequent figures we have reversed the phase(s) of the orbital being subtracted, which is the same as multiplying it by −1 and adding. This gives us Equation \ref{3.7.1b}, where the value \(\frac{1}{\sqrt{2}}\) is needed mathematically to indicate that the 2s and 2p orbitals contribute equally to each hybrid orbital.

\[sp = \dfrac{1}{\sqrt{2}} (2s + 2p_z) \label{3.7.1a}\]

and

\[sp = \dfrac{1}{\sqrt{2}} (2s - 2p_z) \label{3.7.1b}\]

Figure \(\PageIndex{3}\): The Formation of sp Hybrid Orbitals. Taking the sum and difference of an ns and an np atomic orbital where n = 2 gives two equivalent sp hybrid orbitals oriented at 180° to each other.

The nucleus resides just inside the minor lobe of each orbital. In this case, the new orbitals are called sp hybrids because they are formed from one s and one p orbital. The two new orbitals are equivalent in energy, and their energy is between the energy values associated with pure s and p orbitals, as illustrated in Figure \(\PageIndex{4}\).

Figure \(\PageIndex{4}\). each sp orbital on Be has the correct orientation for the major lobes to overlap with the 1s atomic orbital of an H atom. The formation of two energetically equivalent Be–H bonds produces a linear \(BeH_2\) molecule. Thus valence bond theory does what neither the Lewis electron structure nor the VSEPR model is able to do; it explains why the bonds in \(BeH_2\) are equivalent in energy and why \(BeH_2\) has a linear geometry.

Figure \(\PageIndex{5}\): Explanation of the Bonding in BeH₂ Using sp Hybrid Orbitals. Each singly occupied sp hybrid orbital on beryllium can form an electron-pair bond with the singly occupied 1s orbital of a hydrogen atom. Because the two sp hybrid orbitals are oriented at a 180° angle, the BeH₂ molecule is linear.

Because both promotion and hybridization require an input of energy, the formation of a set of singly occupied hybrid atomic orbitals is energetically uphill. The overall process of forming a compound with hybrid orbitals will be energetically favorable only if the amount of energy released by the formation of covalent bonds is greater than the amount of energy used to form the hybrid orbitals (Figure \(\PageIndex{6}\)). As we will see, some compounds are highly unstable or do not exist because the amount of energy required to form hybrid orbitals is greater than the amount of energy that would be released by the formation of additional bonds.

Figure \(\PageIndex{6}\): A Hypothetical Stepwise Process for the Formation of BeH₂ from a Gaseous Be Atom and Two Gaseous H Atoms. The promotion of an electron from the 2s orbital of beryllium to one of the 2p orbitals is energetically uphill. The overall process of forming a BeH₂ molecule from a Be atom and two H atoms will therefore be energetically favorable only if the amount of energy released by the formation of the two Be–H bonds is greater than the amount of energy required for promotion and hybridization.

The concept of hybridization also explains why boron, with a 2s²2p¹ valence electron configuration, forms three bonds with fluorine to produce BF₃, as predicted by the Lewis and VSEPR approaches. With only a single unpaired electron in its ground state, boron should form only a single covalent bond. By the promotion of one of its 2s electrons to an unoccupied 2p orbital, however, followed by the hybridization of the three singly occupied orbitals (the 2s and two 2p orbitals), boron acquires a set of three equivalent hybrid orbitals with one electron each, as shown here:

Figure \(\PageIndex{7}\)). Because the hybrid atomic orbitals are formed from one s and two p orbitals, boron is said to be sp² hybridized (pronounced “s-p-two” or “s-p-squared”). The singly occupied sp² hybrid atomic orbitals can overlap with the singly occupied orbitals on each of the three F atoms to form a trigonal planar structure with three energetically equivalent B–F bonds.

Figure \(\PageIndex{8}\): Formation of sp² Hybrid Orbitals. Combining one ns and two np atomic orbitals gives three equivalent sp² hybrid orbitals in a trigonal planar arrangement; that is, oriented at 120° to one another.

Looking at the 2s²2p² valence electron configuration of carbon, we might expect carbon to use its two unpaired 2p electrons to form compounds with only two covalent bonds. We know, however, that carbon typically forms compounds with four covalent bonds. We can explain this apparent discrepancy by the hybridization of the 2s orbital and the three 2p orbitals on carbon to give a set of four degenerate sp³ hybrid orbitals, each with a single electron:

Figure \(\PageIndex{9}\)). Like all the hybridized orbitals discussed earlier, the sp³ hybrid atomic orbitals are predicted to be equal in energy. Thus, methane (CH₄) is a tetrahedral molecule with four equivalent C-H bonds.

Figure \(\PageIndex{10}\): Formation of sp³ Hybrid Orbitals. Combining one ns and three np atomic orbitals results in four sp³ hybrid orbitals oriented at 109.5° to one another in a tetrahedral arrangement.

In addition to explaining why some elements form more bonds than would be expected based on their valence electron configurations, and why the bonds formed are equal in energy, valence bond theory explains why these compounds are so stable: the amount of energy released increases with the number of bonds formed. In the case of carbon, for example, much more energy is released in the formation of four bonds than two, so compounds of carbon with four bonds tend to be more stable than those with only two. Carbon does form compounds with only two covalent bonds (such as CH₂ or CF₂), but these species are highly reactive, unstable intermediates that only form in certain chemical reactions.

Valence bond theory explains the number of bonds formed in a compound and the relative bond strengths.

The bonding in molecules such as NH₃ or H₂O, which have lone pairs on the central atom, can also be described in terms of hybrid atomic orbitals. In NH₃, for example, N, with a 2s²2p³ valence electron configuration, can hybridize its 2s and 2p orbitals to produce four sp³ hybrid orbitals. Placing five valence electrons in the four hybrid orbitals, we obtain three that are singly occupied and one with a pair of electrons:

The three singly occupied sp³ lobes can form bonds with three H atoms, while the fourth orbital accommodates the lone pair of electrons. Similarly, H₂O has an sp³ hybridized oxygen atom that uses two singly occupied sp³ lobes to bond to two H atoms, and two to accommodate the two lone pairs predicted by the VSEPR model. Such descriptions explain the approximately tetrahedral distribution of electron pairs on the central atom in NH₃ and H₂O. Unfortunately, however, recent experimental evidence indicates that in NH₃ and H₂O, the hybridized orbitals are not entirely equivalent in energy, making this bonding model an active area of research.

Multiple Bonds

In valence bond theory double and triple bonds are formed from unhybridized p orbitals. For example in ethylene (C₂H₄), both C atoms have three bonding pairs and no lone pairs, meaning they are both sp² hybridized, similar to the BF₃ example above. However because C has one more valence electron than B, the remaining unhybridized p orbital is occupied by 1 electron (Figure \(\PageIndex{11}\)). The double bond between the two C atoms is formed because the unhybridized p orbitals on each C atom overlap and form a pi bond, the second bond in a double bond. An sp hybridized carbon would have two unhybridized p orbitals available for pi bonding and could form a triple bond.

Figure \(\PageIndex{11}\): Lewis structure of ethylene (left) and the formation of 3 sp² hybridized orbitals on C, leaving one unhybridized p orbital available for pi bonding. (CC BY-NC-SA; Catherine McCusker)

Example \(\PageIndex{1}\)

Use the VSEPR model to predict the number of electron pairs and molecular geometry in each compound and then describe the hybridization and bonding of all atoms except hydrogen.

1. H₂S
2. CHCl₃

Strategy:

1. Using the Lewis structure and VSEPR approach to determine the number of electron pairs and the molecular geometry of the molecule.
2. From the valence electron configuration of the central atom, predict the number and type of hybrid orbitals that can be produced. Fill these hybrid orbitals with the total number of valence electrons around the central atom and describe the hybridization.

Solution

a. H₂S has four electron pairs around the sulfur atom with two bonded atoms, so the VSEPR model predicts a molecular geometry that is bent. Sulfur has a 3s²3p⁴ valence electron configuration with six electrons, but by hybridizing its 3s and 3p orbitals, it can produce four sp³ hybrids. If the six valence electrons are placed in these orbitals, two have electron pairs and two are singly occupied. The two sp³ hybrid orbitals that are singly occupied are used to form S–H bonds, whereas the other two have lone pairs of electrons. Together, the four sp³ hybrid orbitals produce an approximately tetrahedral arrangement of electron pairs, which agrees with the molecular geometry predicted by the VSEPR model.

b. The CHCl₃ molecule has four valence electrons around the central atom. In the VSEPR model, the carbon atom has four electron pairs, and the molecular geometry is tetrahedral. Carbon has a 2s²2p² valence electron configuration. By hybridizing its 2s and 2p orbitals, it can form four sp³ hybridized orbitals that are equal in energy. Eight electrons around the central atom (four from C, one from H, and one from each of the three Cl atoms) fill three sp³ hybrid orbitals to form C–Cl bonds, and one forms a C–H bond. Similarly, the Cl atoms, with seven electrons each in their 3s and 3p valence subshells, can be viewed as sp³ hybridized. Each Cl atom uses a singly occupied sp³ hybrid orbital to form a C–Cl bond and three hybrid orbitals to accommodate lone pairs.

Exercise \(\PageIndex{1}\)

Use the VSEPR model to predict the number of electron pairs and molecular geometry in each compound and then describe the hybridization and bonding of all atoms except hydrogen.

1. the BF₄⁻ ion
2. hydrazine (H₂N–NH₂)

Answer

Answer a

B is sp³ hybridized; F is also sp³ hybridized so it can accommodate one B–F bond and three lone pairs. The molecular geometry is tetrahedral.

Answer b

Each N atom is sp³ hybridized and uses one sp³ hybrid orbital to form the N–N bond, two to form N–H bonds, and one to accommodate a lone pair. The molecular geometry about each N is trigonal pyramidal.

Summary

Hybridization increases the overlap of bonding orbitals and explains the molecular geometries of many species whose geometry cannot be explained using a VSEPR approach. The localized bonding model (called valence bond theory) assumes that covalent bonds are formed when atomic orbitals overlap and that the strength of a covalent bond is proportional to the amount of overlap. It also assumes that atoms use combinations of atomic orbitals (hybrids) to maximize the overlap with adjacent atoms. The formation of hybrid atomic orbitals can be viewed as occurring via promotion of an electron from a filled ns² subshell to an empty np valence orbital, followed by hybridization, the combination of the orbitals to give a new set of (usually) equivalent orbitals that are oriented properly to form bonds. The combination of an ns and an np orbital gives rise to two equivalent sp hybrids oriented at 180°, whereas the combination of an ns and two or three np orbitals produces three equivalent sp² hybrids or four equivalent sp³ hybrids, respectively. The spatial orientation of the hybrid atomic orbitals is consistent with the geometries predicted using the VSEPR model.

References

1. Kotz, John C., Paul M. Treichel., John R. Townsend. Chemistry and Chemical Reactivity. 7th ed. Australia: Thomson Brooks/Cole., 2009. Print.
2. Shaik, Sason S., Hiberty, Philippe C. A Chemist's Guide to Valence Bond Theory. Hoboken, New Jersey: Wiley, 2008. Print.
3. Wijesekera, Ramanee D. Coordination Compounds: Bonding, Structure and Nomenclature. Oxford, U.K.: Alpha Science International Ltd., 2008. Print.
4. Overlap of Atomic Orbitals to form Molecular Orbitals. http://www.chm.davidson.edu/vce/MolecularOrbitals/overlap/overlap1.html